1. Field of the Invention
The present invention relates generally to computer-generated data visualization.
2. Related Art
Data simulations are now carried out on computers in a variety of applications. For example, data simulations are used in mathematical models of behavior, events, phenomena, or activity or other type of mathematical analysis. Many data simulations involve a number of computations with one or more parameters. In the face of time or processing resource constraints, many data simulations are run using nominal or average values as parameter values in the data simulation. This reduces the accuracy of the data simulation.
For example, in the scientific arts, to simulate various problems encountered, data simulations are generated to analyze the physics involved in a particular problem. For instance, to better enable automobile manufacturers to produce automobiles that will withstand collisions, scientists and engineers run many data simulations in an attempt to discover how to better improve their products. However, due to the many calculations and computations involved in the data simulations, the process is not as accurate as it could be.
For instance, many parameters are used in automobile testing data simulations, such as sheet metal thickness, sheet metal porosity, automobile speed, and angle of impact of a collision. Scientists and engineers often run the data simulations with an average value for some of these parameters to simplify calculations in the data simulations. For instance, standard thickness and porosity values provided by a sheet metal manufacturer may be used in a data simulation even though in practice the actual characteristics of the sheet metal will slightly vary across an actual piece of sheet metal in automobile under test. The scientists and engineers run the data simulations based on the automobile having the standard parameter values due to time constraints of the computer computations. These data simulations, however, do not take into account the various cases in which the parameter values of the automobile vary. For example, it is a known fact in the automobile industry that the thickness, strength, and porosity of sheet metal used to manufacture automobiles vary by as much as thirty percent.
Thus, scientists do not obtain a very accurate overall picture of real life situations. For instance, assume that scientists in the automobile industry are studying the crumbling pattern for sheet metal used to manufacture automobiles. If the thickness of a piece of sheet metal has a Gaussian distribution and the crumbling pattern is symmetric, then the most likely crumbling pattern is not the pattern described by the average thickness of the sheet metal but a thickness offset by a particular lesser or greater amount than that of the value representing the average thickness.
In other type of example, data simulations may be run for a mathematic model which does not have a finite solution for certain parameter values. For instance, most physical processes are described by sets of equations to which there are no analytical solutions. In other words, there is no set of new equations that will exactly describe the result for any given input condition(s). To obtain a solution, scientists and engineers revert to computer models based on an original equation set, and calculate a result for the given conditions numerically. This method involves reformulating the equations to be solved on points on a mesh.
For instance, in weather forecasting, various variables such as wind speed, direction, temperature and pressure are calculated in points on a three-dimensional mesh covering the geographical area of interest and extending into the upper atmosphere. The coarser the three-dimensional mesh, the less accurate the result will be and the ability to predict future weather patterns will be reduced. Given limits in computational power and computer memory, it would not be feasible to use infinitely high resolution. For example, if the grid resolution was improved by a factor of two, a typical computation would require eight times the memory used in a system not engaging in high resolution. Similarly, a typical computation would require sixteen times the computational resources used in a system not engaging in high resolution. Thus, a trade off has to be achieved between accuracy and practical restrictions.
Since some of the physical processes which contribute to the overall behavior of the model occur on scales smaller than the model can resolve, scientists usually account for this by adding this imbalance to the equation set in the form of parametric equations. These parameters are usually tuned in such a fashion that the computational model predicts known cases within a certain tolerance. Nevertheless, there is still a range of uncertainty.
One solution to this problem is to run the calculations repeatedly while varying the parameters, thus obtaining more data simulations and improving accuracy. For example, in the above case of an automobile crash test, this requires a very large number of scenarios for the same automobile impacting the same obstacle, while varying a selected group of parameter values. Each data simulation produces an output dataset. Increasing the number of data simulations, then increases the number of output datasets.
The problem is that scientists and engineers must visualize the data in order to realize where they need to direct their efforts for improvement and further analysis. Due to the very large number of scenarios and data sets involved, it is impractical to view the simulation for every single data set. Further, the more datasets that are generated, the greater the difficulty in obtaining an overview of what is actually occurring.
What is needed is a method and system that provides a visual representation of multiple datasets.